Technical Summary: Hybrid Analytical–EMT Method for HVDC Protection System Component-Level Design

Problem Statement

The design of protection systems for multi-terminal High-Voltage Direct Current (HVDC) grids is complicated by system complexity and conflicting design requirements. Specifically, the component-level design of critical protection hardware—such as DC Circuit Breakers (DCCBs) and series DC inductors—faces significant challenges due to the interdependence of components and the complex interactions between protection systems and converter control strategies.

Existing design methodologies fall into three categories, each with limitations:

1. Analytical Methods: While computationally efficient, they often rely on approximations that fail to accurately represent the complex behavior of HVDC systems, particularly regarding detailed cable and converter dynamics.
2. Simulation-Based (EMT) Methods: These offer high fidelity but require extensive, repetitive simulations (often hundreds to thousands of iterations) to converge on design parameters, making them computationally expensive and time-consuming.
3. Hybrid Methods: Some approaches combine optimization with EMT models, but these still suffer from high computational costs as system sizes increase.

The core challenge is to size DC inductors and specify DCCB parameters (such as operation time and fault neutralization time) to satisfy protection requirements (e.g., fault current limiting, converter overcurrent protection) while minimizing installation costs and avoiding stability issues, without incurring prohibitive computational burdens.

Methodology

The paper proposes an efficient, systematic Hybrid Analytical–EMT Method that integrates fundamental analytical solutions with detailed Electromagnetic Transient (EMT) simulations. The methodology is structured into three main phases:

1. Identification of Critical Cases

To reduce the simulation burden, the method first identifies critical operating conditions that dictate the design:

• Critical Converters: Within each protection zone, the converter that reaches its overcurrent limit fastest during out-of-zone faults is identified. This is typically the converter connected directly to the DCCB or via the shortest line.
• Critical Power Flows: Scenarios resulting in maximum loading of the critical converters (rectifier mode) and DCCBs are selected.
• Critical Fault Types and Locations: The worst-case fault location is determined based on traveling-wave effects and fault neutralization time ($t_n$). Depending on system parameters, the critical location may be a terminal fault or a non-terminal fault along the cable.

2. Core Sizing Algorithm (Iterative Hybrid Approach)

The algorithm treats the DC inductor value ($L_{dc}$) as the primary output variable, while DCCB characteristics and converter capabilities are inputs. The process involves three parts:

• Part A (System Inputs): Defines system topology, protection zones, and DC Fault Ride-Through (DC-FRT) requirements (specifically, that healthy zone converters must not block).
• Part B (Iterative Analytical-EMT):
  • An analytical approximation (Equation 3) is used to estimate the required inductor size based on converter limits.
  • Initially, infeed and cable discharge currents ($\Delta I_{in}$ and $\Delta I_{cab}$) are assumed to be zero.
  • EMT simulations are then run to measure these currents for the specific grid configuration.
  • The inductor value is recalculated iteratively using the measured currents until the difference between successive values falls within a tolerance ($\epsilon$).
  • A similar iterative process is applied to satisfy DCCB current limits (Equation 5).
• Part C (Final Refinement):
  • Recognizing that analytical assumptions (e.g., constant voltage sources, lumped inductors) may lead to conservative (overestimated) inductor values, a refinement step is introduced.
  • The inductor value is iteratively reduced while running detailed EMT simulations.
  • The process stops when a Current Margin Key Performance Indicator (KPI) is met. The KPI is defined as the difference between the maximum allowable current (converter arm or DCCB) and the achieved current, ensuring the design meets requirements with a specific safety margin (e.g., 5%) but is not unnecessarily large.

3. Generalized Algorithm for Multi-Zone Systems

For systems with multiple protection zones, the algorithm is applied to pairs of adjacent zones. The final inductor value for a specific line is determined by the maximum requirement derived from the two adjacent zones it connects. An additional iteration step accounts for the interdependency between nearby inductors, ensuring that the design of one inductor does not negatively impact the sizing of its neighbors.

Key Contributions

The paper outlines three primary contributions:

1. Efficient Systematic Method: Development of a computationally efficient design framework applicable to both fully and partially selective DC protection strategies.
2. Critical Case Identification: A systematic approach to identifying critical converters, power flows, and fault locations, which significantly reduces the number of simulation cases required for design.
3. High-Accuracy Hybrid Specification: A methodology that combines analytical approximations with EMT simulations to achieve high-accuracy parameter specification. This approach allows for the incorporation of vendor-specific "black-box" models, which are often unavailable in purely analytical methods.

Results

The method was validated using two case studies:

• Case Study 1 (Partially Selective Strategy): A five-terminal bipolar system with three protection zones. The algorithm successfully sized DC inductors for various input scenarios (varying DCCB operation times and converter overcurrent ratings). Results showed that depending on the scenario, either the converter arm current or the DCCB current limit could be the limiting factor. The final inductor values ranged from approximately 80 mH to 414 mH.
• Case Study 2 (Fully Selective Strategy): A four-terminal meshed system with ten DCCBs and nine protection zones. The method demonstrated its ability to handle complex interdependencies between multiple inductors. It highlighted that system configuration (e.g., number of adjacent cables) and converter control modes (PQ vs. Vdc droop) significantly influence the required inductance.

Efficiency Gains:
The paper reports a substantial reduction in computational effort compared to pure simulation-based optimization.

• Pure simulation-based methods often require hundreds to thousands of iterations and days of computation.
• The proposed hybrid method required an average of 9 iterations for Case Study 1 and 88 iterations for Case Study 2.
• Execution times were reduced from days to a range of a few minutes to an hour.
• The maximum number of EMT iterations for sizing a single inductor was observed to be six.

Significance and Claims

The authors claim that this hybrid approach provides a practical solution for the industrial design of HVDC protection systems. By leveraging analytical approximations to initialize the design and guide the search space, the method accelerates convergence toward the required parameters. The inclusion of a refinement step ensures that the final design is not overly conservative, potentially reducing installation costs associated with large DC inductors.

The paper emphasizes that the method is robust enough to handle detailed component models, including those from vendors with proprietary control implementations, thereby bridging the gap between theoretical design and industrial application. The results confirm that the method can accurately size components to meet strict protection requirements while maintaining system stability and minimizing hardware costs.